Genetic Algorithm for Solving Spherical Optimization Problems

Optimization of problems which are restricted by non-linear constraints is often difficult. Evolutionary algorithms, in particular, are found to deteriorate significantly in performance on problems that contain non-linear constraints. In this paper, we solve a special class of optimization problems, known as spherical optimization problems, that contain spherical constraints. The spherical constraints are non-linear and can render the problems non-convex depending on how the constraint is defined. It is possible to transform spherical optimization problems from Cartesian coordinate system to Polar coordinate system, which can eliminate the spherical constraints but at the same time gives rise to cyclic variables. To our best knowledge, there does not exist a custom evolutionary algorithm that is capable of handling such spherical optimization problems efficiently. This is a proof-of-concept paper, where we propose a genetic algorithm for solving such spherical problems. The application of the proposed genetic algorithm is not limited to spherical problems alone, and can be extended to solve any optimization problem involving cyclic variables. The proposed algorithm is compared with some commonly used genetic algorithms on a set of test problems with spherical constraints. The results clearly demonstrate the advantages of the proposed algorithm over existing algorithms while solving spherical optimization problems.